IFoA SP5 cheat sheet

Investment and Asset Management: Core Syllabus Reference

• Portfolio return decomposition: total return = income yield + capital gain/loss; real return = (1 + nominal)/(1 + inflation) − 1, or approximately nominal − inflation for small rates.

• Two-asset portfolio variance: σp² = w1²σ1² + w2²σ2² + 2w1w2ρ12σ1σ2; the diversification benefit depends on ρ, not on the assets' individual volatilities alone.

• Minimum-variance portfolio weights for two risky assets: w1* = (σ2² − ρσ1σ2)/(σ1² + σ2² − 2ρσ1σ2); the tangency portfolio maximises (E[rp] − rf)/σp.

• CAPM: E[ri] = rf + βi(E[rm] − rf), with βi = Cov(ri, rm)/Var(rm); beta measures only systematic risk, so idiosyncratic risk earns no premium in equilibrium.

• Bond price sensitivity: Macaulay duration D = Σ t·PV(CFt)/P; modified duration D* = D/(1 + y/m); ΔP/P ≈ −D*·Δy + ½·convexity·(Δy)².

• Immunisation requires matching the present value of assets and liabilities and matching duration; convexity matching gives additional protection against non-parallel shifts.

• Term structure theories: expectations (forward rates are unbiased predictors), liquidity preference (upward bias from term premium), market segmentation, and preferred habitat.

• Arbitrage pricing theory: E[ri] = rf + Σk βik·λk; multiple systematic factors are priced, and no-arbitrage replaces the CAPM's mean-variance assumptions.

• Performance measurement: Sharpe = (rp − rf)/σp; Treynor = (rp − rf)/βp; Jensen's alpha = rp − [rf + βp(rm − rf)]; information ratio = active return/active risk (tracking error).